An Invitation to Universality in Physics, Computer Science, and Beyond

TL;DR

This paper introduces a categorical framework for understanding universality across various fields like physics and computer science, highlighting conditions for universality and its implications such as unreachability.

Contribution

It provides an accessible account of a unified categorical framework for universality, detailing how to identify conditions and compare types of universality.

Findings

Conditions for universality are identified.

Comparison of different universality types is established.

Universality and negation lead to unreachability phenomena.

Abstract

A universal Turing machine is a powerful concept - a single device can compute any function that is computable. A universal spin model, similarly, is a class of physical systems whose low energy behavior simulates that of any spin system. Our categorical framework for universality (arXiv:2307.06851) captures these and other examples of universality as instances. In this article, we present an accessible account thereof with a focus on its basic ingredients and ways to use it. Specifically, we show how to identify necessary conditions for universality, compare types of universality within each instance, and establish that universality and negation give rise to unreachability (such as uncomputability).